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SUMMARY:From Drinfeld-Sokolov bihamiltonian structures to Dubrovin-Frobeni
 us manifolds - Yassir Dinar (Sultan Qaboos University)
DTSTART:20220811T100000Z
DTEND:20220811T110000Z
UID:TALK177143@talks.cam.ac.uk
DESCRIPTION:It is well known that local &nbsp\;bihamiltonian structure (co
 mpatible &nbsp\;Poisson structures) of hydrodynamic &nbsp\;type on a loop 
 space is &nbsp\;the leading term of a local bihamiltonian structure admitt
 ing a dispersionless limit and under certain conditions it defines Dubrovi
 n-Frobenius manifold. We consider Drinfeld-Sokolov bihamiltonian structure
  associated with a distinguished nilpotent element of semisimple type in a
  simple Lie algebra which does not always &nbsp\;admit a dispersionless li
 mit.&nbsp\; We show that its &nbsp\;leading term defines a finite dimensio
 nal polynomial completely integrable system. Moreover\, its reduction to t
 he space of common equilibrium points of this integrable system leads to a
  local algebraic bihamiltonian structure admitting a dispersionless limit.
 &nbsp\; In addition\, the leading term of the new local bihamiltonian stru
 cture leads to an algebraic Dubrovin-Frobenius manifold which &nbsp\;suppo
 rts a conjecture due to Dubrovin about their classification.
LOCATION:Seminar Room 2\, Newton Institute
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